Here for example embedding a video to a blog post. Prerequist is that you’ve no fear to change some html source.

• Upload the video to the Files application in Connections
  • All blog readers need to have access to the video file
  • Easiest way is to upload to Community files and use it in the Community blog directly in this community
• Open the file within IBM Connections Docs Viewer and click on ABOUT – Get Links

  

• Copy the “Link to download file:” to the clipboard

  

• Now create a new blog post (add heading, tags, additional text)
• Switch to the HTML view in the post

  

• On the position where you want to add the video, add following source:

<video src="url from files viewer" controls="" width="640px"></video>

• Example:

<video src="https://connections.example.com/files/form/anonymous/api/library/6722626c-b14c-4f4e-80fc-f27f71ad2cb9/document/512adfd2-1d30-4a3d-92ee-13db1f5f0574/media/2018-01-22%20Call%20February%202016.mp4" controls="" width="640px" height="480px"></video>

• Post the document

  

Update

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Thanks to Urs for the comment, I updated the code so it is valid XHTML now.